I had this exact same problem, the battery fully depleted and when I went to charge it the only thing that would happen is a vibration every couple seconds, nothing would come up on the screen.
I held the volume, home, and power buttons and booted into recovery mode and just hit reboot device, I didn't need to do the reset. I am back up and running now.
Probably going to upgrade to a new model though, this one has been giving me trouble. Sensor issues, screen goes black like it thinks it's on a table and you're not using it, or up to your ear when on a call, but I'm not. Even disabled the bs features and still does it..